## Power Functions

A power function is when we have any variable x to the power of any real number represented here as n.

In the formula sheet we are given the equation:

So basically all we do is multiply our function by the power term and then minus one the power term by one.

### Power Function Differentiation Example

Say we have x to the power of negative fraction:

We still follow the same procedure of multiplying the function by the power term and then minus it by one.

## Polynomials

A polynomial is basically a combination of power functions. So while they may appear to be more tricky, if we isolate each term, they are just as easy as the example above.

### Polynomial Differentiation example:

Given the equation below find the derivative:

you first need to rewrite it so that it looks more straightforward:

Then just follow the simple rule: bring the power down, put it in front, and take one away from the power.

Lets start with first term:

The second term:

The plus 4 at the end of equation is eliminated, as it has no x component.

To find we simply add these terms together

**Exponential Functions**

The exponential functions that we focus on in maths methods is

This is Euler’s number to the power of a variable x and has a remarkable differentiation property

## Exponential Differentiation

In the formula sheet we are provided with the very useful formula:

** **

This is one of the easiest rules to follow as all you do is multiply the exponential component by the coefficient of x

### Exponential Differentiation Example

Let’s try to find the derivative for this function

** **

If we follow the formula provided, it greatly simplifies the process

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